Question: Simplify the following expression: $z = \dfrac{a^2 - 14a + 45}{a - 9} $
Explanation: First factor the polynomial in the numerator. $ a^2 - 14a + 45 = (a - 9)(a - 5) $ So we can rewrite the expression as: $z = \dfrac{(a - 9)(a - 5)}{a - 9} $ We can divide the numerator and denominator by $(a - 9)$ on condition that $a \neq 9$ Therefore $z = a - 5; a \neq 9$